Abstract
In this paper, we are interested in the study of non-Archimedean quasitriangular operators and their relation to the invariant subspace problem.
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References
M. Aguayo and M. Nova, “Non-archimedean Hilbert like spaces,” Bull. Belg. Math. Soc. Simon Stevin 14, 787–797 (2007).
Y. Amice, “Interpolation \(p\)-adique,” Bull. Soc. Math. France 92, 117–180 (1964).
C. Apostol, “Quasitriangularity in Hilbert space,” Indiana U. Math. J. 22, 817–825 (1973).
C. Apostol, C. Foia and D. Voiculescu, “Some results on nonquasitriangular operators,” Rev. Roum. Math. Pures Appl. IV, 285–312 (1973).
W. B. Arveson and J. Feldman, “A note on invariant subspace,” Michigan Math. J. 15, 61–64 (1968).
M. Babahmed and A. El Asri, “Invariant subspace problem and compact operators on non-Archimedean Banach spaces,” Extr. Math. 35, 205–219 (2020).
T. Diagana and F. Ramaroson, Non-Archimedean Operator Theory, Springer Briefs Math. (Springer, Cham, New York, 2016).
R. G. Douglas and C. Pearcy, “A note on quasitriangular operators,” Duke Math. J. 37, 177–188 (1970).
P. R. Halmos, “Invariant subspaces of polynomially compact operators,” Pacif. J. Math. 16, 433–437 (1966).
P. R. Halmos, “Quasitriangular operators,” Acta Sci. Math. 29, 283–293 (1968).
G. R. Luecke, “A new proof of a theorem on quasitriangularoperators,” Amer. Math. Soc. Proc. 36, 535–536 (1972).
P. Meyer-Nieberg, “Quasitriangulierbare operatoren und invariante untervektorraume stetiger linearer operatoren,” Arch. Math. (Basel) 22, 186–199 (1971).
L. R. Narici and E. Beckenstein, “A non-Archimedean inner product,” Contemp. Math. 384, 187–202 (2005).
C. Pearcy and N. Salinas, “An invariant-subspace theorem,” Michigan Math. J. 20, 21–31 (1973).
C. Perez-Garcia and W. H. Schikhof, Locally Convex Spaces over Non-Archimedean Valued Fields, Cambridge Stud. Adv. Math. 119 (Cambridge University Press, Cambridge, 2010).
W. Sliwa, “The invariant subspace problem for non-Archimedean Banach spaces,” Canad. Math. Bull. 51, 604–617 (2008).
A. C. M. Van Rooij, Non-Archimedean Functional Analysis, Monograph Textbooks Pure Appl. Math. 51 (Marcel Dekker, Inc., New York, 1978).
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El Asri, A., Babahmed, M. Non-Archimedean Quasitriangular Operators and the Invariant Subspace Problem. P-Adic Num Ultrametr Anal Appl 14, 325–334 (2022). https://doi.org/10.1134/S2070046622040069
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DOI: https://doi.org/10.1134/S2070046622040069